Universal credit

I had to give up my job last year on the 5th of May 2020 due to my health issues. I was in receipt of the disabled element of my WTC and CTC I was sending my sick notes to the DWP and I couldn't get them on the phone, this was just when lockdown was kicking right in. I eventually had to claim for UC as it was advertised constantly on the TV and radio on the 11 of July 2020. I am enquiring about should my claim for UC been passed as I was or should I say would be getting Contributiion based ESA also I should have been awarded a disability premium in my UC. I repeatedly asked my UC work coach about my sick notes and how I was receiving WTC and all she said was Why are you sending sick notes? I didn't get awarded my ESA until the start of September 2020 and if I hadn't claimed UC I would have been receiving my contributions based ESA from the start of my first sick note and also better off.